Properties

Base field \(\Q(\sqrt{2}) \)
Label 2.2.8.1-2450.2-g
Conductor 2450.2
Rank \( 0 \)

Related objects

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Base field \(\Q(\sqrt{2}) \)

Generator \(a\), with minimal polynomial \( x^{2} - 2 \); class number \(1\).

Elliptic curves in class 2450.2-g over \(\Q(\sqrt{2}) \)

Isogeny class 2450.2-g contains 3 curves linked by isogenies of degrees dividing 9.

Curve label Weierstrass Coefficients
2450.2-g1 \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 27 a - 3180\) , \( -49883 a - 67\bigr] \)
2450.2-g2 \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( -23 a - 5\) , \( -178 a + 123\bigr] \)
2450.2-g3 \( \bigl[1\) , \( a + 1\) , \( a + 1\) , \( 2 a\) , \( 5 a - 7\bigr] \)

Rank

Rank: \( 0 \)

Isogeny matrix

\(\left(\begin{array}{rrr} 1 & 3 & 9 \\ 3 & 1 & 3 \\ 9 & 3 & 1 \end{array}\right)\)

Isogeny graph